Please help me.... the question is:

Question

the angle of elevation from one point on the street to the top of a building is 29*. The angle of elevation from another point on the street, 50 feet away to the top of the building is 25*. To the nearest foot, how tall is the building?

Answer 1

tan(29°) = h/x
tan(25°) = h/(x+50)

h = x tan(29°)
h = (x+50) tan(25°)

x = h/tan(29°)
(x+50) = h/tan(25°)
x = h/tan(25°) - 50

h/tan(29°) = h/tan(25°) - 50

h/tan(29°) - h/tan(25°) = - 50

h(1/tan(29°) - 1/tan(25°)) = - 50

h = 50/(1/tan(25°) - 1/tan(29°))

h ≈ 146.86049049385 ≈ 147 feet

check:

x = h/tan(29°)
x ≈ 146.86049049385/tan(29°)
x ≈ 264.94333821349035 feet

tan(29°) =? h/x
0.554309051452769 ≈? 146.86049049385/264.94333821349035
0.554309051452769 ≈ 0.55430905145277 √

tan(25°) =? h/(x+50)
0.466307658154999 ≈? 146.86049049385/(264.94333821349035+50)
0.466307658154999 ≈? 146.86049049385/314.94333821349035
0.466307658154999 ≈ 0.466307658155 √

Answer 2

Hi Becky;

Within 4-degrees (29-25), 50 feet has passed.  This is (12.5 feet) per (1-degree).  The initial angle at the bottom of the building is 90-degrees.

[(90-29) degrees][(12.5 feet)/(1-degree)]

[(61) degrees][(12.5 feet)/(1-degree)]

The unit of degrees is in the numerator and denominator.  It cancels...

[(61) degrees][(12.5 feet)/(1-degree)]

(61)(12.5 feet)

762.5 feet

A triangle is now formed with 762.5 feet as its base.

One angle of the triangle is 29-degrees.

The second (bottom of building) is 90-degrees

The third (top of building) is 61-degrees.

The tangent of 29-degrees is its opposite side (height of building) divided by its adjacent side (762.5 feet).

Tangent of 29-degrees is 0.55.

0.55=x/(762.5 feet)

Cross-multiply...

419.375=x

The building is 419.375 feet tall.

 

The tangent of 61-degrees is its opposite side (762.5 feet) divided by its opposite side (height of building).

1.80=762.50/419.375

1.80≈1.80